The invention relates to an artificial intervertebral disk member having an upper and a lower support, which are attached in the adjacent upper or lower vertebra, and having an elastic separator between the upper and lower support. Such intervertebral disk members are known from EP-A-0 317 972, for example. This intervertebral disk member is implanted in the centre of the adjacent vertebral body. So as to maintain the required mobility of the vertebral column and of the vertebral bodies respectively, this intervertebral disk member is by necessity substantially smaller than the cross section of the adjacent vertebral bodies. However, as a result, the loading in the pressure-sensitive centre of the vertebral bodies is so great that they are damaged and that the intervertebral disk member sinks deeper and deeper into the vertebral body as time passes. Thus its function is impaired more and more, and additional damage can occur. A further important disadvantage is that this known intervertebral disk member can not successfully be adapted to the special characteristics of the patient such as weight, condition of the bone substance and position of the intervertebral disk to be replaced in the spinal column. Thus, this artificial intervertebral disk member does not fit very well even at the beginning of the implantation and becomes even worse over time.